My favorite setting was, far and away, Planescape ... so maybe I am a bit biased, but the more I think about this, the better it seems.
I love RPGA, and I love LFR ... but what I love about it is more the way it is played, and the way it -could- be played, not necessarily the setting. Like most people that are playing and running a lot of LFR, I see the same two main issues of complaint coming up the most: 1) The disconnected feeling of the adventures, where characters are flung all over the world, and 2) character races that don't "fit" the setting. So far the second complaint is mostly about Warforged, but my feeling is that when new settings come out, with races designed specifically for a setting some RPGA players are going to want to play them, and some RPGA players are going to make a stink about them not being "Realmsy".
The potential behind a Living Planescape Campaign would be pretty limitless, and I can only see that being a good thing. Whenever a new D&D product comes out, the options would be available and legal for the campaign. This would A) generate interest and sales in all products - making WotC happy, B) give complete freedom of lots of choices and options to players - making the section of the market that lots and lots of options appeals to (most of us) happy, C) ensure that the people that buy the books would definitely be able to get their money's worth (no problems of - "Yes, you paid good money for your Dark Sun setting books, but you can't play a Thri Kreen from Cormyr, sorry.") - making paying customers happy, and D) all this would be accomplished without upsetting those of us who can get a touch irritable or disappointed when the feeling of story immersion is lost due to "flavor breaking" elements such as Thri Kreen from Cormyr or Warforged from the Dales.
Also, the problem of the adventures feeling less connected and making less sense than most episodic serial television dramas could be taken away completely, without detracting at all from the wonders of fantastic, varied, and far-flung settings and backdrops for the adventures. With Sigil as the home base, the very nature of being an adventuring Planeswalker means the characters get to go all over the place and do all sorts of things, without any of it feeling cheapened or "unrealistic".
And there's so much more ... think of the Factions! (By the way, if WotC brings back Planescape without bringing back the Factions in all the height of their 2E glory I will be sorely disappointed.) Anyway ... think of factions kind of like the way Regions currently work in LFR, only better. When a player makes a Planeswalker character, they choose a faction to join up with, gaining some kind of small, flavor-based mechanical benefit. But they could be a lot more. The factions could be completely player driven, and almost guild-like. Using the interwebs players could "connect" with the community of their Faction. There are so many great ideas here - Imagine if something along the lines of "Story Awards" were implemented, but when you earned them with your character by doing stuff in the mod, you were also earning them for your faction. When a group gets together at a con or weekly event, they all want to work together for the good of their party obviously, but they're also individually out to bring home glory for their Factions. Some sort of point or award or ranking system could be implemented to see how the various Factions were in relation to one another, maybe even affecting the fiction. (I always loved how L5R used the winners of their tournaments to determine which clans were in power.) This would bring a healthy and interesting level of competition to the game without upsetting the feeling of cooperation, and if implemented the right way could really make each individual player feel like they were taking part in a "Living" breathing campaign.
And that's just the tiniest bit of my ideas of how awesome this could be. But I don't want to over-rant. What do you guys think?
I am also prepared to engage in a lengthy siege of WotC headquarters and/or replace key members of their personnel with loyal robot look-a-likes to ensure that my predictions come true.
From them, I have heard tales of the various campaign settings.
Planescape and Dark Sun both interest me greatly, and I would LOVE for those settings to be updated so that a newbie like me could play and/or run. (I'm about three months to starting my first DMing experience. We need to finish another campaign first.)
I really hope a 4E "Living Planescape" comes to pass. I can't stop thinking how cool everything about that would be, and I know the community would be great. Haha, I'm such a dork, but I love when I run across another Planescape-fan and we start speaking in cant, while the poor clueless look on like we're both barmy.
@ibixat: That's horrible about losing your collection.
I had the complete run as well (even the comics and little extras), a few pieces were even signed by T.D. After falling on hard times a couple years ago, I ebayed the whole lot ... except for the Conspectus poster which is still hanging on my wall. 
I know R&D watches the boards ... more than a few of the suggestions made by forum posters made their way into the new FR setting. So if anybody else thinks this would be a good idea, why don't we try to keep this thread alive? Anybody got any other ideas for a Living Planescape community, or maybe just for Planescape 4E in general? One thing I personally would like to know is how important the Factions would be to you guys.
I don't know how it would work out as a campaign starting at level 1 though, I'd really need to see how they'd adapt the setting. I really hope they do though.